book-recommendations

[mortal iris]

Probably the most productive year of my life late into my undergrad.

Sounds like something I would utterly dislike lol

[wheat remnant]

FIS Linear algebra or Mathematics for machine learning? thoughts on choosing one over the other? I don't know if I have the energy at this point to do the rigorous proofs in FIS, I'm familiar with the concepts, but if there's a more concise way that gets me to that finish line for AI/ML without having to just grind proofs and examples would this text be it?

I'm pairing this with blitzsteins probability and I've taken a good amount of discrete courses in the past so those areas I'm not massively concerned with, just the application of tensors with linear alg and machine learning but I don't want to shoot myself in the foot by cutting corners, not to mix metaphors

[molten gulch]

FIS is good, I like it purely because it has the proofs and computations

[wheat remnant]

yeah its an awesome book! just super massively dense with the proofs and examples, which is great, but may be overkill for the amount of time i would need to dedicate to it to grind it to its fullest, and if I can get to the same spot for application without having to do that that would save me boatloads of sanity and etc hahahahah

claude suggested math for machine learning deisenroth but i figured i would ask a human too

[tame tree]

theres no getting around proofs and lots of work if you want a good knowledge of linear algebra

[wheat remnant]

how long would you give yourself to grind that

[tame tree]

that depends entirely on you and your background

[wheat remnant]

i mean of course, but

generally speaking, put an hour or two 2 or 3 days a week, how many months or so

i'm not totally looking for mastery, just application within modeling and machine learning contexts

[tame tree]

just work through the textbook

these types of questions are, imo, a waste of time

you can skip these sections for ML and be fine probably

[tame tree]

you'll probably not get very far with that amount of time invested though

[wheat remnant]

yeah i understand that sentiment-- i'm just thinking from a certain mindset that a given college course is 10 weeks, if i just work through the book in that would-be timeframe, I think grinding all the proofs and examples is just overkill for what i would need and would take 6 months

[tame tree]

college semesters are typically closer to around ~14 weeks

[wheat remnant]

right, exactly-- and that my question comes to really, is that worth it for my purpose kind of thing--do i absolutely need to have linear algebra completely cold mastered to be able to train models at a professional level and is this the only text that gets me there

[tame tree]

i don't know what your purposes are nor do i work in ML, the people who have phds in these fields absolutely do have a very solid foundation of linear algebra though

there's just not any escaping it

the entire thing is pretty much fancy linear algebra

[wheat remnant]

a lot of it is matrix expansion, i'm currently finishing chapter 2 with FIS and the context of everything pre-matrix to me i dont see the point in grinding through proof wise

[tame tree]

those concepts better help you understand matrices

[wheat remnant]

honestly the context of matrices make way more sense to me than proving independence of linear transformations

[tame tree]

what do you mean by "independence of linear transformations"

[wheat remnant]

and of course because everything after this chapter is matrices it probably picks up but

[wheat remnant]

that's literally one of the questions, bottom of page 74

[tame tree]

this?

you don't call a single linear transformation "independent" unless you're considering it as the singleton vector {T} in L(V,W)

anyways

you could probably also read the linear algebra portions of hubbard and hubbard and be fine

these are less general than the settings FIS works in

[wheat remnant]

yeah i dont know, josemon youre kind of making me want to continue with this for achievements sake

youre right. I think I'm going to do this then, and skim through FIS and go from there

[hybrid sigil]

Can’t you study linear algebra “on demand”? I.e. see what exactly is needed for your particular ML needs (say to understand a paper or technique) and then try to learn exactly that and then move down the dependency tree?

That would theoretically guide your study progression in a motivated way

[wheat remnant]

i could! honestly probably a great method, i always feel weird doing this because i dont feel like i have a foundation but thats a me thing and this is smart

[hybrid sigil]

Yeah, not denying the benefits of building the foundation, but you seem to be bored with that and not certain about its value now, so may be worth trying something else, given that you have such a practical attitude

It’s also possible that this “on demand” method would just lead to the same result: need for the solid foundation

But it remains to be seen

[wheat remnant]

yeah that's all very true--I've taken a linear algebra course in college before, i did well in it, but it stopped after eignvalues and eigenvectors, and it was a few years ago. i feel like i need a tune up and would like a good foundation because I know the roles I want use it, its just getting into that shape I'm wondering if it will pay off mainly

[hybrid sigil]

Are you talking about engineering roles in ML, or doing some research?

I suspect the engineering roles won’t require much math even in ML

[wheat remnant]

engineering roles that lead to ML yeah

[wheat remnant]

i really dont know how much it does, i have a friend who did a phd in ai, and his paper was in linear algebra matrices and he doesn't use a whole lot of it now which to me is insane

[hybrid sigil]

It’s probably just setting up some pipelines, combining various libraries, trying various parameters, until it works, etc. :)

[wheat remnant]

that's kind of why i'm like do i really need to hit every single proof in this book

[tame tree]

theres a bit of a gulf between AI/ML practitioners versus researchers

[wheat remnant]

yeah its pytorch and tensor manipulation with data

[hybrid sigil]

I suspect your recent course in LA may be already fine for that

[tame tree]

(as is the case with every field)

[wheat remnant]

yeah as of right now (within the next 3 years) I probably will not be looking at research, and if I do ill just lapdog whatever my grad school wants

[wheat remnant]

i hope so, i do need a tune up i think, i just got owned by josemon's rebuttal earlier up lol

[hybrid sigil]

Yes, I think ML engineering just sounds sexy but in fact it’s not much different to other engineering

[tame tree]

probably a lot of the job is software engineering / data science without a bunch of fancy maths (this is just based on what friends have told me)

[wheat remnant]

yeah i couldn't agree more. i'm reading FIS along with a probability book, and a python book right now just grinding all of this in parts

[blazing holly]

Late to this, but i’d focus on learning linear algebra and stats for their own sake (without it being in contest to ML)

That way you are less stressed about your journey & once you eventually learn enough, the dive into ML is practically free

[odd cargo]

wheres this problem from

[tame tree]

FIS

[narrow bloom]

Any good books for self studying diff top / diff geo?

Oo thank you I’ve heard of that Lee book before

What is your opinion on the exercises in that book?

/ also janich

Oh ok wait that’s good

Yes same

Wait that’s pretty epic

Thank you

What abt janich?

Hm I see

Would you say it’s better to do that one first

/ what dyt are the relevant chapters of lee since im looking at it and it looks quite long

Or would you say they’re all important

Gotcha

Oh I see that’s sick

Nicee

I think I’ll check it out then ty for the rec

Oh I see thank you

For some reason I did AG before doing DG

LOL

But this is prob good nonetheless

Noice

Lowkey don’t know what a pencil is ngl

I should learn more AG too

Argh

Noice

Have u read Shafarevich?

Ngl I tried self studying out of that book and didn’t rlly like it much

Oh I see

Oh like basic algebraic geometry I

Didn’t realize he had a nt book

Oh wow really

Maybe I should check that out too then

So many things to learn

[odd cargo]

pretty sure he has a free course on it on youtube too

dude has a lot of videos

[velvet flax]

symbolic integration I by bronstein seems somewhat interesting

[frozen wave]

I am starting physics, any recommendations?

[blazing holly]

Since this is your first exposure, just use the text that your physics class is using

[frozen wave]

I am in ninth grade

I think I have a solid base in caculus

I just bought a book on Morin, is it too early?

[tame tree]

read halliday resnick krane, physics vol. 1

[blazing holly]

Wait just so we’re clear
Are we talking precalc or actual calc?

Since highschool physics doesn’t really employ the later

[frozen wave]

Why would I say pre calc

[blazing holly]

(Well maybe if you’re in a school which has E&M physics)

[frozen wave]

True

I want to study Quantum mechanics rigorously, but I know I need a good foundation, and it will mostly be self study, it would be a great help if you have any recommendations, I humbly request

[blazing holly]

Sometimes students mix up the two so i just wanted clarity

Early physics classes are heavily algebra based so I assume you’ll be fine w/ your calculus background

[mortal iris]

It depends on where you are.

[frozen wave]

For my school physics is in 12 grade

[mortal iris]

Where I come from Calculus based physics is the norm in high schools albeit done rather poorly

[frozen wave]

Isn’t it most schools?

I might be wrong

[mortal iris]

It depends on where you are from

[frozen wave]

And biased

[mortal iris]

And curriculum, etc.

[frozen wave]

True

But why algebra heavy?

[mortal iris]

What makes you think so? Can you solve mindless problems or can you actually write some proofs?

[blazing holly]

Yeah
My college has both algebra based & calc based for students

[frozen wave]

I think I am good at writing proofs

[mortal iris]

Calculus is a pretty steep hill to climb

[cunning elk]

even algebra based physics is taught hideously poorly at most schools

[frozen wave]

Nah

[mortal iris]

Have you done any epsilon-delta proofs?

[cunning elk]

my AP phys 1 “teacher” was prob the worst teacher I’ve ever had the misfortune of being in a class with

[blazing holly]

He doesn’t need proofs for physics man, cmon

[frozen wave]

No

[midnight gulch]

do you need proofs for a first physics course?

[narrow girder]

Morin for a beginner in physics is hell

[frozen wave]

T too much

[mortal iris]

No. This isn't for a first physics course

[frozen wave]

I mean not too often

[mortal iris]

I'm a physicist and I say otherwise.

[blazing holly]

No
You don’t need proofs if at all in physics

[frozen wave]

Nice

[cunning elk]

ok try deriving Maxwell’s equations then

[mortal iris]

At the early stages only

[blazing holly]

Hyperbole

[frozen wave]

I mean I really really want to understand physics deeply

[cunning elk]

at the early stages everything is super oversimplified anyway

[frozen wave]

So I hope I can get a good rigorous text

Oooof

[blazing holly]

Forgot pdes

[tame tree]

oof indeed

[mortal iris]

I would recommend going through Mathematical Analysis by Zörich. If you've done some calculational stuff in Calculus and are confident in it, you should be able to handle these two volumes. You'll learn most of what you need for mechanics and electromagnetism as well in due course of the books. And see hints of QM too when you do Fourier.

Besides this you need a linear algebra book. Consider working through Axler or FIS alongside Zorich. It's also very helpful to have some background in Abstract Algebra with a book like Judson.

[tame tree]

the top 3 things to focus on to make physics go smoothly at this stage are: linear algebra, calculus (including multivariable calculus), and odes

[frozen wave]

Do you mind if I ask whether there might be a book that has overlap in application for physics and hard rigorous proofs like Apostle

I know it’s quite a lot to ask

[midnight gulch]

apostle?

[frozen wave]

Like

Hey

“Like”

[mortal iris]

I just mentioned it. Also Apostol*

[frozen wave]

Oh

[cunning elk]

try kleppner for mechanics?

[blazing holly]

Go for physics texts targeted towards mathematicians

[frozen wave]

Wait is anyone familiar with AOPS?

[normal crystal]

The Apostle of Physics
sequel to The Tao of Physics

[mortal iris]

Mechanics and electromagnetism usually needs differential geometry in those.

[frozen wave]

Frick

[cunning elk]

too familiar

[frozen wave]

Frick

Frick

[mortal iris]

What the Frick is Frick?

[frozen wave]

So should so do math and physics in parralel more?

I was thinking mastering the math then when good base do the physics

[mortal iris]

Just complete Zorich. You'll be more than ready to do physics rigorously from there.

[frozen wave]

Okay

[tame tree]

doing math first is honestly not a bad idea

[cunning elk]

your first E&M studies will be greatly enhanced by knowing multivariable calculus

[frozen wave]

I mean you can get the inter connectivity of doing both in parralel

[tame tree]

i've read a few physics texts where the explanations border on schizophrenic but knowing the math properly made things easy

[mortal iris]

Upto differential forms, because holy hell are the equations elegant lol

[blazing holly]

How strong is your calc knowledge currently @frozen wave?

[frozen wave]

I honestly don’t know how to gauge it

Like a standard school course I can do

But you mean some competition problems getting there still to be fluent

[blazing holly]

State some topics your comfortable w/

[mortal iris]

Not necessary if you have a math text that uses physics examples as motivation and has physics problems in the exercises like a Zorich.

[blazing holly]

Competition math, no

[frozen wave]

What you mean no

[cunning elk]

a standard calc 1/2 course is entirely non rigorous

[blazing holly]

That’s a entirely seperate skill

[mortal iris]

It will make your Calculus rather strong as well

[frozen wave]

You sure

I just dive in and proof

[tame tree]

you can learn a lot of "theoretical physics" in passing from examples/deliberations in math texts

[frozen wave]

I can’t tell the difference

[tame tree]

but you should probably read some "proper" physics texts as well for mechanics and EM

[frozen wave]

Who?

Sorry to ask

So plan is Zorich or Apostle

[tame tree]

what does the inquiry "who?" regard here

[mortal iris]

They are largely haphazard imho. It's more useful to learn the physics in a lab and the math from a math text.

[frozen wave]

Whether your regard was to who

Well should I consider lectures?

[tame tree]

right, but some of the exercises at least develop the sort of physics problem solving that the mathier texts aren't necessarily trying to train

[frozen wave]

I am hoping to have more topics to study in one day and rotate

[mortal iris]

Nothing ideal exists for what you need besides Zorich to my knowledge. I do not recommend it lightly. It is heavily physics driven but with rigor on par with Rudin.

[frozen wave]

Well Apostle has a lot of application problems, and in the right context isn’t it just physics?

[tame tree]

any time i venture back into physics i get bored whenever experiments/real world application gets brought up

[mortal iris]

It's Apostol*

[blazing holly]

Competition math problems are structured differently from typical calc problems. Its more like a tool of the trade

That’s why im asking you to give general statements of your current calc knowledge(differentiation, integration, etc.)

[frozen wave]

Sorry

[cunning elk]

precollege competitions don’t include calculus as a general convention

hmmt used to have a calculus round but that was phased out a while ago

[mortal iris]

That depends on what you need really. Some physics problem solving is necessary for sure but one can do so after analysis and linear algebra.

[wicked fractal]

Do yourself a favor and stay away from competition math. Pick a book on abstract algebra instead

Or real analysis whatever

[frozen wave]

Why do you say that?

[cunning elk]

they’re two completely different things

[blazing holly]

Since its a whole different process

[wicked fractal]

Let me ask you the following: why do you do competition math?

[frozen wave]

The same reason why I do math

For fun

Hmm

Why is no one active

[blazing holly]

I’m here
I was waiting on deltoid lol

[frozen wave]

Oh

[wicked fractal]

Have you ever thought why the "tricks" you use work as you wanted them to be?

[frozen wave]

You know each other?

[cunning elk]

“dead chat” after 5 seconds of no one typing ahh response 😭

[frozen wave]

I don’t use tricks I figure the problem out myself

It’s faster

[wicked fractal]

[frozen wave]

Dead monkey

Nah

[blazing holly]

We all use tricks all the time
The entirety of integral calculus is learning tricks to do integrals

[frozen wave]

Okay

For you’s response

Thanks

[wicked fractal]

The number theory questions that are often in math competitions just make me want to cringe

[frozen wave]

Mind if I ask if all of you are post graduate?

[blazing holly]

Woah, wouldn’t diffgeo be kinda overkill at their current level?

[blazing holly]

Im a late undergrad

[frozen wave]

Oh

I am in ninth grade

[blazing holly]

They still need to do linear alegbra, multivariable calc & the likes

[frozen wave]

Is Morin too much for starting physics?

I just bought the book

I might be done for

[blazing holly]

Yes
An introductory physics book is more than enough as a start to the subject

[frozen wave]

Ooof

Feel like a noob

Wait did any of you use Morin?

Any tips would be helpful

The classical one

Classic

[blazing holly]

As an introductory text, the one by Freedman & Young would be my recommendation

Then look for textbooks in areas that you’re interested in for a comprehensive dive(iirc you mentioned QM)

[frozen wave]

Hmm

Woah you have gotten to Quantum mechanics already rigorously?

Okay

[blazing holly]

I am taking my first QM course now actually
Mathematical rigor isn’t expected at this stage

[frozen wave]

Oh

[blazing holly]

Honestly i expect that appears when you reach graduate, and maybe even phd level

[frozen wave]

Is there any chance I can out reach people in my area like in Cambridge to give advice as well?

They seem busy

Really

[blazing holly]

You can always shoot an email, though responses are never guaranteed

[frozen wave]

They would admit a scrawny boy under their wing?

Hmmm

Nice shooting it down

True

Very true

I have been self studying all through this point

[blazing holly]

Honestly, i’d start w/ talking to your physics teacher
“Hey this is way below my paygrade, could you and I spare some time after class to discuss more intensive physics”?

Smth like that

[frozen wave]

I have a environmental science teacher

Physics is 12 th grade for me

Senior

I am freshmen

Barely into high school

[blazing holly]

Its still possible to just talk to the teacher for said class

[frozen wave]

True

[blazing holly]

Just head to their classroom/office

[frozen wave]

I think they have PhDs

[blazing holly]

And say you’re interested in physics & show you have background in calculus

[frozen wave]

Okay

And plus

[twilit pulsar]

maybe they'll introduce you to Ricci flow

[frozen wave]

The universities near me are Harvard and MIT like should I ask them for advice

I should wait outside the door and track them down should I?

I am short, and they will think I lost my parents

[blazing holly]

?
I thought you were in the Cambridge area?

I is dum

[frozen wave]

No in Lexington

But near I meant

Sorry for the misunderstanding

You sure

[tame tree]

please stop doxxing yourself

[twilit pulsar]

i second math circles also yeah

[frozen wave]

Okay

I will try

[midnight gulch]

there is the mit primes summer program, though it is very hard to get in

[frozen wave]

Yea

[midnight gulch]

idk about the boston area specifically but also look into community colleges to possibly take math/physics since you're interested

[frozen wave]

How do you get into the good math circles though

Like I know they will deviate, but I do not think too much

[tame tree]

arent they open to the public?

[frozen wave]

You have to send application

I think

[tame tree]

oh and these cost money too, lovely

a bit gross imo

i thought all math circles were free public events

[frozen wave]

You can often get the money cut

[midnight gulch]

there is this https://promys.org/programs/promys/for-students/application/

[frozen wave]

Oooooooof

Let’s see

How much

What do you consider a challenging problem set?

For the math circle

And that is what I try to solve and submit?

[midnight gulch]

i assume they are looking for something competition math related, though im not sure since ive never done any of this math circle stuff

[frozen wave]

So like fluent in IMO level?

[midnight gulch]

no definitely not lmao

[frozen wave]

Really?

I can not apply to PROMYS yet bro

It says I need to complete ninth grade first

[midnight gulch]

yeah, i don't think you should either. your time would (probably) be better spent taking core classes at a community college / program

[frozen wave]

In what context

I learn faster by self studying

Or deeper

[midnight gulch]

and it means nothing because you dont get credit for the class

you can self study and take classes at the same time, if you're further ahead then it will just be even easier

[frozen wave]

Well I am quite ahead

I just basically sleep in class

True

Some have very different ways

[midnight gulch]

also you haven't taken a university math class before from the sounds of it, not the same as high school

[frozen wave]

Oh

How is it strutted differently?

Structured

[midnight gulch]

much faster paced

[frozen wave]

I just pick up a textbook and go with it I don’t know what level I am

But I try to choose textbooks that are rigorous

Well nice meeting you all, I have to sleep.

The advice was very helpful, and I am thankful

Yep

[velvet flax]

foundations of mechanics by abraham, marsden, and ratiu

[cedar crypt]

I believe Insel Friedberg and Spence is better than Kunze

[remote knoll]

Marion and Thornton

wait, that might be too much reading up

9th grader presumably doing 9th grade math? I guess any kinematics based physics book would be a decent introduction, but will likely be challenging with the amount of math you have.

[remote sparrow]

murasugi's knot theory book is a translation

[remote sparrow]

https://www.rxddit.com/r/math/comments/1q22bmm/dummit_foote_solutions_manual_in_progress/

[hybrid sigil]

Looks like a useful project

[hybrid sigil]

Are you serious? Recommending this to someone in 9th grade?

[frozen wave]

I do not only know ninth grade math

[hybrid sigil]

I mean: that book that was recommended to you is quite hardcore from the look of it, it's for people who at least completed their undergraduate university degree. My comment was not meant to belittle your knowledge or abilities. It's just that recommendation seems completely inappropriate

Quoting from the book's preface:

The basic audience for the book remains the same: mathematicians, physicists, and engineers interested in geometrical methods in mechanics, assuming a background in calculus, linear algebra, some classical analysis, and point set topology.

Are you a mathematician, physicist or engineer interested in geometrical methods in mechanics? I doubt it.

But if you like the book, go for it, of course

[narrow girder]

uh..... I highly do not recommend a beginner in physics hit THIS up, not in the least because this is so math-heavy "mechanics" is an honorary term
(this is Abraham et al.)

[hybrid sigil]

that's what I meant. It just looks that @velvet flax has fun recommending difficult and challenging books left and right. Books like this one, or Kobayashi/Nomizu, or Dieudonné

[floral lantern]

Any book would work for learning the physics, but I would recommend doing the problems from David Morin’s “blue book”

Red Morin in my opinion is too difficult for a first course in physics (even with a strong basis in calculus) and the blue book problems ease you into tough physics problem-solving

[tender cobalt]

Marsden Foundation in Mechanics?

[narrow girder]

yes

[vernal ore]

Just picked up a non-standard analysis book, but I don't understand the first thing about Abstract Algebra. Any book recommendations?

[tender cobalt]

Artin Algebra

[vernal ore]

Thanks. Any prerequisits?

[hybrid sigil]

Pinter "A book of Abstract Algebra"

no pre-reqs, just enjoy the ride :)

it also has some neat applications in the Problem sets -- like automata theory or error codes

not very deep, but may be entertaining

[vernal ore]

Nice, thanks for the recommendations!

[hybrid sigil]

What is that "non-standard analysis book" you are reading? @vernal ore

[vernal ore]

Something in portuguese. I think it's an introductory book

It defines infinitesimals, has some references to historical uses of infinitesimals, and has some exercises. I have only read the introduction and first chapter, but one of the exercises asked me to prove some stuff about maximal ideals and isomorphisms, wich while I know one or two things about these concepts, don't know enough to write proofs

Anything wrong with it? I picked it up because I like learning about infinitesimals xd

Thanks for the recommendation too!

I meant anything wrong with non-standard analysis?

[dapper root]

Have a dream and learn it in your sleep

[twin zinc]

ive been sticking to aluffi algebra chapter 0 for a while but upon looking at the fields chapter i feel like it doesnt cover enough to get my foundation squared off to study ant does anyone have any (preferably freely available from the author) recommendations for field theory to supplement what i study in aluffi

[dapper root]

I’m not gonna lie

I think most people learn the field theory stuff in an ANT book

[twin zinc]

ohhh

yea that does make sense

i was just looking for perhaps some supplementary material

that looks toward things like

local and global fields

abs vals

cool thanks

also my analysis is a wee bit rusty is that gonna be a big problem for me in ant

or is it more something i could brush up on without any huge issues

thats pretty fair

i anticipate i will definitely have to for modular forms

but im not gonna be engaging too much with that for a while

[dapper root]

I think there’s a book by Serre called local fields. It’s probably really difficult

[twin zinc]

yeaaaa it looks like i could pick through it super slowly but id constantly have to cross reference to remind myself of some of the stuff its saying

which knowing me i wouldnt last long in that scenario

[tender cobalt]

Only proof writing

[molten gulch]

https://www.jmilne.org/math/CourseNotes/FT.pdf
https://www.jmilne.org/math/CourseNotes/ANT.pdf

[robust egret]

Halliday fundamentals of physics

[tame tree]

fundamentals is considerably worse than “physics”

[robust egret]

Have u even seen the book?

I can attest that the mechanics chapters helped me in my countrys physics olympiad

Halliday fundamentals of physics extended covers mechanics, waves, thermodynamics, e&m and modern physics at an introductory level but its calculus based

[tame tree]

yes ive seen both books which is why im saying that

fundamentals is a newer pared down version of their older “physics” text

[robust egret]

Whats wrong with the fundamentals of physics textbooks?

[tame tree]

the exercises are a bit worse

its overall more surface level in every aspect

[robust egret]

What about university physics by young and freedman?

[tame tree]

ive never read it

[molten gulch]

similarly meh

all the intro physics books are similarly meh

IMHO why not just go read taylor's classical mech if you know calculus

[robust egret]

Well theyre intro level

[robust egret]

What if u wanna cover more than mechanics?

[molten gulch]

then griffiths' electrodynamics

or if you're a bit mad, just use jackson

[robust egret]

Why the hell would someone do jackson as their introduction to e&m

[molten gulch]

and then there's blundell for thermal physics, pathria for stat mech, shankar or sakurai (or griffiths again) for qm

peskin and schroeder for qft (tho I've heard conflicting accounts of how good and recent it is for qft)

[molten gulch]

My dad did when he was in India about 30 years ago it was the standard for intro EM

apparently

[robust egret]

Thats wild

[mortal iris]

It's bad. Pretty bad. The only reasonably good introduction is Sydney Coleman's with Talagrand's being a close second. But if you are willing to go a bit hardcore then Weinberg is solid. Peskin & Schröder is one of those infamous terrible "standard" texts.

[mortal iris]

It's entirely doable if you have a strong calculus background upto vector calc.

The problems are just infamously challenging.

But there are easier problems in there too.

[mortal iris]

I'll give the Feynman's Lectures a pass for intro level though but they don't come with a solid problem set sadly. But if someone uses the lectures properly and makes problem sets based on them, it's a solid intro physics course.

[tender cobalt]

That's what I did

Actually a pretty good idea

The problems are good enough and the theory is actually properly motivateda nd feels like real physics

Compared to intro books

[tender cobalt]

Holy shit

[tender cobalt]

Holy shit

How to get strong calculus background upto vector calc

I wanna join teh cool kids club by learnign from Jackson

[marble solar]

It has a legendary reputation, and that's about it

[chilly wolf]

I would like to ask, are there videos that is meaningful for each chapter in complex analysis to guide u understand easily and proof?

[tender cobalt]

Richard bocherd's videos are pretty nice

[chilly wolf]

Sure ty

[past barn]

Salut/Hi Im french so i would like to have some books recommendations (In french please) je suis en 2nd générale

[velvet flax]

i thought it was obvious that it was a joke

i dont think anybody actually reads that book

if u care about the geometric viewpoint, you read arnold

if you super care about it

you just know it by osmosis

[hybrid sigil]

fair enough

[hearty pollen]

I think Landau's vol1-10 is severly underrated. I've found my approach to learning is getting an idea of the big picture (or atleast an outline) and then filling it in instead of (or only then) building things up like a tower. With just classical mechanics you can introduce action as a generating fxn then base space with TQ,T*Q->symplectic->poisson geometry->geometric quantization. I'm currently brainstorming how to teach this to motivated highschoolers so I definetly believe it's possible. Rigorously though you'd need diff geo, but you can build a lot of intuition with lin alg imo and supplement rigor as you learn more

[floral lantern]

You can just read Griffith.

A lot of people say “read a linear algebra based qm book first to learn it right”

And there are merits to this

But ultimately QM is a departure from classical physics and I find the best way to learn it is to shut up and calculate

Through Griffith you’ll get an idea of what doing QM and solving QM problems is like

And later you can read a book like sakurai and get an understanding of the historical development

[wanton pollen]

amazon.. wtf???

well yeah it was the page i was on

[buoyant silo]

Omg my mom made me study sacred geometry with her and I just wanted to cry the entire time, they have no clue what they're talking about 😭

I mean I understood it, it was all just completely false

[dapper root]

Sacred geometry is real.

Lowkey, when I tell laypeople I do algebraic geometry every once in a while someone tries to talk to me about sacred geometry and I’m just kinda like

https://tenor.com/view/the-office-michael-scott-yikes-ahh-grin-gif-12951381

[buoyant silo]

I mean, the 'lectures' were on YouTube. My mom is deeply into astrology and mystical such, so I think she was just anamered by all the whimsical words
(She has zero understanding in actual math)

[wanton pollen]

yeah i know its a thing but "recommending" (sponsoring) it under an actual math book is odd, to say the least.

[dapper root]

My message was a meme

[remote sparrow]

yo that middle book is from the guy that had super hot ai-generated korean women on the covers for a time before they toned them down to be less horny

[dapper root]

You can tell because I put a period at the end of the sentence

[wanton pollen]

🤔

why have sacred geometry if real geometry is sacred

[buoyant silo]

Let me say this about sacred geometry:
It's interesting to study if you're into folklore and history, but treating it like modern science is, well, you know

[mystic silo]

any good textbooks for bc calc, like that go super in depth into all topics

[midnight gulch]

stewart

[mystic silo]

what version is the best?

[midnight gulch]

i prefer the older versions, but they are all very similar

like i have the 2nd edition which is from 1990 iirc

[mystic silo]

does it cover both calc 1 2 and 3?

or not both i guess but u know what i mean lmao

[midnight gulch]

yeah from precalculus to multivariable

[mystic silo]

alr thanks

[nova canopy]

Lol why is there a random girl on the cover????

[wanton pollen]

clicks

[remote sparrow]

the covers used to be even hornier

[nova canopy]

Oh no whyyy

[tender cobalt]

Just start zorich like @mortal iris suggested

It has physics applications

and it's the best book to use right now

If you're looking for rigor + physics applications

[wanton pollen]

holy shit lmao

(side tangent but who the hell trademarks the phrase "1-click"?)

[tender cobalt]

LOL

Perhaps it's a company of Clickbait specially

[mortal iris]

One click to buy them all

https://tenor.com/view/d-gif-2374314719452959720

[wanton pollen]

i can buy 50 GTM books at once! thanks amazon!

[high grotto]

https://tenor.com/view/мультсборник-gif-19336312

[remote sparrow]

yeah here's an old screenshot

[pearl palm]

How do these not get taken down?

And if not for the cover then for being slop in general

[vital chasm]

Amazon doesn't care

[pearl palm]

That makes sense

I remember seeing those books too

There’s so many

[vital chasm]

With AI as it is now its all too easy to make these garbage

[twin parrot]

https://tenor.com/view/creality-3d-printer-3d-printing-thanos-reality-is-often-disappointing-gif-4200832396039209558

[violet portal]

Any good books on knot theory

[remote sparrow]

your background?

[heady ember]

If you don't understand intro Algebra, I'm guessing you haven't learnt mathematical logic either?

If so, you should also pick that up unless your NSA book covers logic from the ground up..

Algebra: see the pinned message of recommendations. Personally I like Jacobson's Basic Algebra I. (Basic != Easy)

Logic: look in pinned for 's recs. Ebbinghaus and Rautenberg are well-liked, from what I gather.

[remote sparrow]

https://people.math.wisc.edu/~hkeisler/

if you have some prior familiarity with real analysis, you can read some of Lectures on the Hyperreals: An Introduction to Nonstandard Analysis by goldblatt

https://link.springer.com/book/10.1007/978-1-4612-0615-6

[signal zenith]

There is a semi popular math YouTuber who dropped off the face of the earth and sold a million AI slop textbooks on Amazon and started making videos abt being a passport bro in SEA lol

Anyway yeah Amazon doesn’t care

[remote sparrow]

the math sorcerer yeah?

is the philippines considered SEA tho

[midnight gulch]

yeah

[pearl palm]

Math sorcerer?

[vital bane]

It's actually considered to be land

[mortal iris]

Yes

[mortal iris]

ISlands

[midnight gulch]

those are pacific islands, but "pacific islanders" is typically used as a more specific racial term

[chilly wolf]

I would like to ask, are there videos that are meaningful for each chapter in Quantum Mechanics to guide u understand easily and proof in second year (beginning)?

[hybrid sigil]

Hot take: oceans are just big salty lakes!

[mortal iris]

What do you mean by guide u understand easily and proof?

Counter-example. Europe.

[vernal ore]

Thanks for the logic recommendations too!

[pearl palm]

Really big peninsula

[mortal iris]

Depends on what you mean by really big since by that logic India should be a continent.

Also this is assuming that a peninsula is defined as a landmass surrounded by water on at least 3 directions as opposed to exactly 3.

[nova canopy]

LMAOOOOO

[nova canopy]

Me doing math lmao /j

[mortal iris]

This is all the motivation I need to give the horny teens in my class to study calculus

[odd cargo]

eulers got it for sure.

[tender cobalt]

Relatable af in indian schools

[mortal iris]

Make that Indian schools for rich brats

[tender cobalt]

but public school kids are also like that lol

im in some low-mid range english medium school and i can say all the guys here are just down bad af

which you only observe in public schools

[mortal iris]

Well I am dealing with a private school with rich kids

[tender cobalt]

English medium school?

[mortal iris]

And coming from a public school environment myself I can vouch that this is not as true in South India as it's in the North.

[tender cobalt]

rich kids are actually worse in the sense they feel empowered for everything

[mortal iris]

And I've had the privilege of being in both places

[tender cobalt]

I see

[tender cobalt]

U will see them doing meetups for no reason, wasting parents money on everything

[mortal iris]

With kids losing their virginity by 6th grade up in the North

[tender cobalt]

holy shit

[mortal iris]

And virgins roaming the south even in their 30s

Lol

[vital bane]

you can't make a blanket statement like that about everyone 🥀

[mortal iris]

Private schools here rarely offer anything else

[vital bane]

some are bad, some are good, it's not black and white

[tender cobalt]

in indian subcontitent its mostly bad if youre a rich brat in a private school 🙂

[tender cobalt]

oo

is it international curriculum

[mortal iris]

I'll have to defend some of my students here tho. Some genuinely good kids. Very clever ones too. One is a bit too clever cos he's doing diff geo and functional analysis despite being in 11th grade. Another is an Olympiad qualifier.

[tender cobalt]

Damnnn

THat's pretty good

These ones are rare af

Sadly I can't find anyone with similar mindset like me at all

[mortal iris]

No. One of the central ones.

[tender cobalt]

0 people in the entire school willing to study pure math/physics

Altho I found people via the olympiad community

still not really,

[tender cobalt]

do you discuss about pure math with that kid 🥶

i wish i had a teacher like you

[mortal iris]

Let me also put this outside of math. There's one kid who made a pretty cool drone by himself. One is making a mini refrigerator with a fully digital console using rather basic equipment. One is trying to work on an open statistical physics problem experimentally.

[tender cobalt]

That's awesome man

[mortal iris]

I do. He recently asked for help with a proof on locally compact groups. I should get to it actually.

Oh there's a couple of 12th graders who are incredibly gifted in biology. One wants to study immunology and has already worked with some postdocs at a top institute in India.

[tender cobalt]

🥶 🥶 🥶 🥶 🥶 🥶 🥶

Meanwhile there are 0 talents in my school 🙂

The math club is shit

The science club is shit

Everythings shit

Students are just brainrots

[mortal iris]

I'm using ours to teach 3 kids linear algebra lol

[tender cobalt]

Struggles with algebra based physics in A levels

[tender cobalt]

wow

[mortal iris]

One of them is a 9th grader

[tender cobalt]

let's take this to #math-discussion

[mortal iris]

Nothing to discuss really. I gtg anyways

[tender cobalt]

alr

[proud osprey]

That last part is very inappropriate wtf?

<@&268886789983436800>

[mortal iris]

Look at the context of the discussion?

[tender cobalt]

??

[mortal iris]

But sure I see the point in how this can be misunderstood lol

[astral meadow]

I think in the context it's more or less fine, as @mortal iris said. Perhaps very clumsy, so be careful for misinterpretation next time though!

[mortal iris]

Yeah. I realised. Hence edited it.

[odd cargo]

Never seen this dude type in this chat ever.

i am now convinced that there're people here who exist solely to @ mods when they see something they deem outside of their "boundary for respectability politics".

[molten gulch]

Yes, to be completely honest, yes there are, many of us lurk all of the chats in the server periodically looking for things gone wrong when we don't have anything substantive to talk about

[mortal iris]

These poisons are everywhere lol. On both ends of the political spectrum. One end is likely to complain. Another is likely to troll.

[twin parrot]

You guys have math and science clubs?!?

My school doesn't

What do you have to say🙂

[tender cobalt]

eca lol

non functional

[weary remnant]

@mortal iris khan academy vs precalculus by stewarts?

[wicked fractal]

Khan academy

[weary remnant]

And for calculus a book is required right?

[wicked fractal]

Khan academy

[weary remnant]

You did KA?

[mortal iris]

It depends on what you want.

[weary remnant]

Get to calculus and do physics

[mortal iris]

There are still two routes. You wanna do it the traditional physics way or the proper math way?

Basically do you prefer guesswork and trickery or reasoning and proofs? Both very much related to each other tho.

If it's the former, then khan academy all the way.

[weary remnant]

I kinda want it to be easier when I get to college

[mortal iris]

You can supplement with any books that you like for extra problems and practice

[mortal iris]

It would be easier in either way. One is just gonna train you to study physics the way your average physicist would. Another is gonna train you to study physics in the way a mathematician would.

For the second route you pick up Lang's Basic Mathematics. Work through the book. Alongside Proofs by Cummings. Then jump into Zorich's Mathematical Analysis alongside Linear Algebra by FIS.

[weary remnant]

Not going to that path haha 😅 I think it’s just going to be fun to just do them for fun, because I am weak with my mathematics

[mortal iris]

I should add that the latter route is typically the harder one.

[mortal iris]

Well, I found the latter route pretty fun myself although I used different resources and had a slightly more confusing start cos I tried to do too many different things.

But to each their own ig.

[mortal iris]

If you're not so great at math and wanna do physics, try to build things at home as opposed to just playing with equations and videos.

[weary remnant]

I do have serge lang’s basic mathematics but it is really dry and it ends up stocked in my bookshelf

[mortal iris]

You can buy a breadboard and some electrical equipment quite easily. Maybe even learn how to work with an Arduino and a Raspberry Py

[weary remnant]

Im more on doing HRK mechanics and then griffith and etc morin

I just need the tools to solve Ipho problems

Specifically physics olympiad

[mortal iris]

It may seem dry to the mathematically untrained for sure. Perhaps consider Axler instead then for Precalc.

[mortal iris]

If your math is bad why you bothering with a Physics Olympiad? Also what's with this hype about competitive exams for no reason? You're not learning or gaining much doing them.

Unless you're like top of the top

Which requires intense preparation

[weary remnant]

My math is bad on the top level but is good on the average level

[mortal iris]

You can spend time trying to tinker and play with diy ideas and hone experimental intuition rather than obsessing over theory for no reason.

[mortal iris]

That sentence makes no sense and this conversation is infuriating.

I think I need my dinner

[twin parrot]

He intends to ace physics olympiads with a weak foundation in math

Interesting tho

[chilly wolf]

Like just to understand the concept and explanation

[arctic wedge]

can anybody recommend an algebra 2 book thats easy to understand and simple?

[wanton pollen]

lang algebra

[mortal iris]

If you want videos, look at Barton Zweibach's MIT OCW Lectures on Quantum Mechanics. If you want a book, pick up Cohen-Tannoudji's Quantum Mechanics. You are expected to have a background in single variable and vector calculus along with linear algebra. Also basic classical mechanics and electromagnetism.

[vital bane]

Most but not all

[mortal iris]

What do you typically intend to cover in Algebra 2?

These things differ from place to place yk. Please stop defaulting to names where you are from.

[violet portal]

I have a phd and I would like to learn the advanced side of knot theory

[remote sparrow]

lickorish, rolfsen, manturov

[arctic wedge]

factorization, polynomials and inequalities, functions (domains) and quadratic equations and sequences

[arctic wedge]

alright my bad

[wet sentinel]

thats what i call a good recommendation

[midnight birch]

Does anyone know a good textbook for re-learning Laplace transforms?

[remote sparrow]

boyce and diprima?

https://complexanalysis.org/howell-complex-analysis-web.pdf

the laplace transform in the more general complex variables setting is discussed here in chapter 11

[midnight birch]

🙏

[tender cobalt]

i dont understand yall physics olympiad participants

you just think that if you memorize the math formula and tool that youre gonna automatically be able to "apply the tool" in problems

thats just a misconception, you can't

Like

What is stopping you from picking up a calculus book and actually learning the math?

it doesn't take long

You will spend more time scratching your head on the math part of every physics problems

That is going to slow you down much more than spending 2-3 weeks to properly learn the math

pick up a book like stewart or thomas and just learn the math, it doesnt take much effort and its not that difficult. If you can't learn math from a book like stewart/thomas and want to use math as "tools" still, then forget about physics lmao , this is just the basic foundation you need to get right before tackling everything . WIthout the basic mathematical skills you will keep getting stuck in physics

[tender cobalt]

If you don't learn calculus properly from a textbook

You'll struggle a lot from morin Taylor Griffiths etc

By a lot

I mean you will literally just be stuck on the math and forget about all physics

Become fluent in the math, no need for proofs or whatever

Just get good enough at math that you don't need to worry about the physics

When you can stop worrying about the math while approaching any physics equation, that's when you're ready

Plus you dont need anything beyond basic calculus and some vector calculus to solve the problems

[mortal iris]

Stitz and Zeager's College Algebra is good.

[mortal iris]

It does. It takes quite some time to learn things properly. Unless you are just cherry picking for results.

[arctic wedge]

thanks

[tender cobalt]

It took me 2 months to learn single variable calculus from thomas

including a lot of other useless stuff contained in it like applications

which if u skip it shouldnt take more than 1 month to learn calculus

[mortal iris]

And you wouldn't know how to prove IVT from there

[tender cobalt]

yeah and im not telling him about proof based

im telling him about learning computations

the basic stuff

hes doomed if he skips over even those

[mortal iris]

Even using it as a tool it's tricky. Also physics necessarily needs upto multivariable Calculus.

[tender cobalt]

well was telling him the bare minimum he needs

since something like purcell teaches the multivariable on the way

U can pick those up on the way

Tbh

But if u don't have basic calculus fluency

Learning the formulas will not help in physics

You'll get stuck in the math

That's what I'm saying

It's kinda absurd to say about "using the tools" at this beginner stage lmao

You need algebra trigonometry and calculus to even comprehend what's going on , it's the bare minimum

It'd work to learn those from khan academy as well

But in the end, still need to learn

Whether from Stewart or whatever

[mortal iris]

As someone who started off this way I thoroughly disagree. Physics can often pull a fast one at you and throw something you have no idea how to deal with regardless of this pick it up as you go kinda fluency and then they'll tell you that we need Bessel functions to solve this and what not.

I'd rather learn the math first. Properly. So that ik how to think about what I'm looking at. You need a healthy mix of both proofs and calculations.

And be able to use a computer for most of it to check how stuff works if you don't yet have an intuition for it.

[wheat field]

anybody have good recommendations for learning measure theory?

[vital chasm]

First three chapters of Folland's Real Analysis

And the chapter on Lp spaces if you need

[mortal iris]

Cohn's Measure Theory is pretty good. If you want a hardcore comprehensive look then Bogachev.

[tender cobalt]

Same here

[latent thorn]

Anyone have a book to recommend for pre university mathematics. English, french or russian as preference if it is possible. Without exercices just pure lessons

[mortal iris]

Mathematics without exercises is pointless.

[latent thorn]

I just want 2 seperate book. And id like to find first one with lessons on it. Idk if it exists

[mortal iris]

Why? How's that helpful?

[rocky sphinx]

Yeah how

[latent thorn]

Ask my school 😭

They give u the lesson and then exercices

[mortal iris]

But you're the one asking for it?

[rocky sphinx]

Dumb ass school

[latent thorn]

So i thinked about a book that may have plenty of lessons

[mortal iris]

That makes zero sense. You need to check your understanding before moving on to the next subtopic always.

For which exercises are vital

[rocky sphinx]

You cant do math like that

[latent thorn]

Well am not gonna only read lessons

I will exercices on each lesson which is very obvious

[mortal iris]

Then you don't need separate books

[latent thorn]

Its just a preference, if you guys have a nice book to recommend id just go with it

[cunning elk]

im of the opinion that you dont really need a dedicated book for standard precollege topics but eh

[mortal iris]

It depends on what you cover at the pre uni level.

[mortal iris]

Depends on the student and their faculty at school too.

[cunning elk]

online resources on those topics are super oversaturated already in any case

[cunning elk]

ig

[latent thorn]

Tbh I am not the best in math and id like to see the basics again and go higher and higher after. Rn am in computing network and electricity

And I realise that I am never rly confident abt basic math and waste to much time on each problem

[mortal iris]

This is even more confusing. So you're an undergrad who wants to go back to pre uni math?

[latent thorn]

Am in high school

[mortal iris]

Then what's with computing network and electricity? What's that gotta do with learning pre uni math?

[latent thorn]

Because I have mathematics and am terrible at it. And in the future id like to do more mathematics

Am basically here ^

[mortal iris]

Okay. That doesn't help much. If you wanna be better at math then pick up Serge Lang's Basic Mathematics to begin with. Also his Geometry book for high schoolers and also Proofs by Cummings. Having Hall and Knight's Higher Algebra can be handy.

[latent thorn]

Am sorry I try my best to explain, english isnt my first langage

[latent thorn]

Okay thanks u, am gonna check if its available in my country

[mortal iris]

Not the problem. Idk what you have covered or intend to cover. High school programmes differ depending on countries. That said what I've suggested is on average what's done in most places, but poorly.

Alternatively you can also pick up Axler's Precalculus.

Alongside Cummings' Proofs.

[latent thorn]

Maybe this will help, its the average academic program of most private schools in my country:

[latent thorn]

I will try to find french versions if it exist. But I don't mind of some books are in english

[kind flume]

Try The Joy of X @latent thorn

it's not that algebraic nor technical

[gray gazelle]

try cengage mathematics by g.tewani

[kind flume]

but it's very good and walking through where math is useful in the real world and that insight into how to spot patterns and systems etc. is the reality of what math is about

[gaunt cave]

you should learn cathegory theory

[latent thorn]

Mh I see

[desert oriole]

no

[latent thorn]

Ah

[desert oriole]

you should do exercises

[desert oriole]

"an invitation to mathematical logic"

[latent thorn]

Okay

[kind flume]

i just closed category theory 😉

[latent thorn]

I dont understand anything from the book

Like every symbol look like egyptians scripture

like what is this ??????

[desert oriole]

oh nvm

[latent thorn]

this is just scary rn

am still struggling with equations

[desert oriole]

.

[latent thorn]

okay okay

[mortal iris]

Pop math is not math. That type of book is for a beginning middle schooler or someone who doesn't know a wink of math.

[kind flume]

it's not about the math in it, it's about the pattern recognition and the application of math

[mortal iris]

Irrational indeed.

[kind flume]

which are far more important skills than being able to recall formulae by rote

[mortal iris]

Then it's better to pick up something like The Art and Craft of Problem Solving but more so as a supplement to Lang and Cummings.

[kind flume]

i'd say complimentary 🙂

[mortal iris]

Aye sure. Can function either way.

The thing is pop math gives the wrong idea to students. Same as pop physics. It glorifies the stuff without really letting you go through the grind. Hence it's not a great idea for older students to read through pop math.

[kind flume]

is the grind really so valuable?

i know for some it's a key aspect for learning by doing

but it's not prescriptive

[mortal iris]

It very much is. How else do you learn?

[kind flume]

observation

intuition

plenty of thoeries on the huge array of human learning invention

[mortal iris]

Leads you to problems like Russell's paradox in math parlance.

[mortal iris]

Cannot always be done without specialised equipment or high level of mathematical machinery.

[kind flume]

it depends on what skill we want to be testing for really - it's analogous to exams v coursework

the theory is the same but what we test is different

abiliity to recognise a pattern or regurge fundamental knowledge under pressure of time vs being able to illustrate a problem and explain it comprehensively

the domain matters almost more than the content

[mortal iris]

Well. If you're learning math to be better at it then you have to learn how to read math, write proofs and do calculations. All of them. It's just that our standards of what evaluates to good differs depending on what level of study you're at.

[kind flume]

i disagree that's just one angle of math

[mortal iris]

There's three in case you didn't count.

[kind flume]

that the industry rewards the format of that collection of production has no bearing on whether an individual can demonstrate understanding in a fundamental way

[mortal iris]

These things are built into the three.

[kind flume]

if your proof is sound semantically, it's sound. you do not need math as well. it's just that math as a language is built with these descriptions in mind.

it's far easier to say and demonstrate Cogito Ergo Sum in latin than it is in algebra.

[mortal iris]

Well I am not speaking of any industry tbf. It's about how one evaluates where they are in terms of mathematical aptitude.

[kind flume]

that's my point, aptitude is not a value we should attach to the work - it's a value we should attach to the person

and if the person can't read, that doesn't mean they can't reason

bit of a paradigm upheaval i know

[mortal iris]

That wouldn't constitute a proof to begin with. It would be an argument.

Arguments can be countered, regardless of validity.

Proofs, only if they're flawed.

[kind flume]

this is just semantics

CES is known to be a fundamental truth of the universe

however we express it, however the format is defined - it's still true, self-causing, evident

[mortal iris]

No it's not. There are radical skeptic arguments against it for instance (BIV)

[kind flume]

if i do an e-d proof of a concept, is that any lesser than a more standard assumption axiomic approach?

is Wiles' proof of Fermat worse for not being that elegant?

if it's proven it's proven

[mortal iris]

Rigor is not about what tools you use to prove things but whether you prove things correctly. This is a pointless argument since we don't expect rigor from high schoolers but rather open up a path for them to be rigorous.

[kind flume]

that people argue against it doesn't invalidate its truth - people argue for simluation theory all the time and we can prove that to be false

[mortal iris]

Another pointless tangent.

[kind flume]

you're talking about correctness of a method not correctness of the answer

rigour is an arbitrary definition

it has use

and by extension utility

[mortal iris]

No I am not. You are by bringing in epsilon-deltas

[kind flume]

but it's just a random choice of the way things are

the same way you format a submission based on the journal - the content is irrelevent to the knowledge

[mortal iris]

No it does not. It's pretty well defined in the sense that every proposition used in a proof must ultimately go back to the axiomatic systems you work with.

[kind flume]

i didn't say poorly defined, i said arbitrary

[mortal iris]

And you are just arguing for the sake of an argument. Not studying pop math has nothing to do with rigor it's about not creating false expectations.

Because you don't learn math from there. You learn about what ppl learned from math there.

[kind flume]

which proof style do you endorse? this i am genuinely intertested in because i am in the process of reviewing my work and it would be i feel helpful to explore different ways to show my results

[mortal iris]

And in a haphazard manner nonetheless.

[kind flume]

i have a semantic version, minimal algebra, a formal algebraic construction and an e-d extension

what is good to help other people understand my theory

[mortal iris]

Doesn't matter so long as it's correct. But if you've gotten it right then I'd expect you to revise it to make things concise, elegant but at the same time explanatory.

[kind flume]

it's beautifully elegant

4 statements, 5 axioms and complete

but the consequences are far reaching and i know it's going to be a challenge for people to accept some of the implications - assuming i haven't complete botched the algebra; but i can't see how

one of my former professors is reviewing it atm

[mortal iris]

What's an e-d extension?

[kind flume]

it extends the concept to the level of Schema

i hadn't done one before, some 23 principles you have to demonstrate the system operates under

[mortal iris]

I see

[kind flume]

often used in dyanmical systems

which is one of the applications of the result here

[mortal iris]

That's what corollaries to propositions exist for.

Either way, this has gone beyond the subject of book recs.

[kind flume]

very true

but enjoyable discourse nonetheless, thank you 🙂

[mortal iris]

Likewise although for a bit I was confused as to what the point of it was.

[kind flume]

to have it in the first place 😄

[pearl palm]

How do you gain intuition without the grind?

[kind flume]

by observing the universe

the world around us all

[pearl palm]

You’re gonna have a hard time fully observing the universe without math

[kind flume]

you can't fully observe anything

even with math

[muted tide]

hey

can sm help me

[hybrid sparrow]

To ask for mathematics help on this server, please open your own help channel or help thread. See #❓how-to-get-help for instructions.

[tender cobalt]

whats good about axler's precalculus

[tender cobalt]

Bro I got the perfect subject for you

https://en.wikipedia.org/wiki/Teleology

And I also got the best youtube channel for you: https://www.youtube.com/@NewCalculus (GUYS DONT FOLLOW THIS)

[subtle nymph]

Book recommendations for calculas, algebra, coordinate geometry, trigonometry and Vector/3D for exams like Jee Advanced [questions added for reference]

[gray gazelle]

whats wrong w it??

[molten gulch]

Indian books are tailored for the indian curriculum, besides that, they just vomit problems at the reader with almost no proper exposition of topics

[mortal iris]

Also having been a misguided idiot who used it before, there are many errors in there that are easy to miss for the untrained eye.

[gray gazelle]

hmmm true

[mortal iris]

Just use the materials from the coaching centers you're paying for.

And solve an endless number of problems.

Look for books when you wanna learn something as opposed to for a formula vomit and guess the trick exam.

[kind flume]

oh yes i did philosophy at school 😄 but i'm more of a practical existentialist

[wanton pollen]

[verbal hamlet]

anybody knows a book full of problems for calculus, like something to practice

[wanton pollen]

i have one from like 1970

i could send it via carrier pidgen

[mortal iris]

Solve exercises from Spivak.

[rough umbra]

unrelated to the discussion at hand, why do you think wiles' proof is not elegant?

[kind flume]

i find it interesting but it relies very heavily on mapping across the various domains

i see his skill is how how he identified the map that kind of zoomed out perspective

nevertheless the reality is difficult to approach for the majority because it relies so greatly on a large number of disleperate knowledgebases

[shy nymph]

Hey guys I’m new, does anyone have any good books they’d recommend on practicing probability and data analysis?

[rough umbra]

i don't think the majority of people have to understand something for it to be elegant

[latent thorn]

Hey so for like hours based on guys answer to my request. I managed to find the books and did analyze them with the help of A.I and with the academic program of my country i made a logical list of everything I should know and should review step by step with exercices tell me what you think about the order !

2. Numbers & Calculations
   → Sets
   → Operations
   → PEMDAS
   → Signed numbers
   → Percentages

3. Algebra
   → Algebraic expressions
   → Equations
   → Systems
   → Complex numbers

4. Functions & Analysis
   → Definitions
   → Reference functions
   → Differentiation
   → Integrals
   → Convexity

5. Sequences
   → Arithmetic
   → Geometric
   → Recurrence

6. Geometry
   → Plane geometry (Pythagoras, Thales)
   → Trigonometry
   → Areas / volumes
   → Analytic geometry
   → Dot product
   → Space geometry

7. Statistics & Probability
   → Statistics
   → Basic probability
   → Tree diagrams
   → Distributions (binomial, normal)

its based on the mosts recent grades classes i went @mortal iris @gray gazelle

[mortal iris]

AI involved. Me no talk

[latent thorn]

What's wrong with A.I

It is a good assistant to scan multiple pdf that has 400 pages

[shadow vector]

thoughts on this book? https://link.springer.com/book/10.1007/978-3-031-84977-0 looks incredibly cool no?

It seems kinda like Arnold's mechanics book just more accessible

[gray gazelle]

why is basic geometry and trig so far down
why not introduce the basics of functions earlier
I don't think following a program cobbled together by an AI is better than following a program cobbled together by people? why wouldn't you just grab a sample degree program from a university's website and mimick the order of their courses?
seems weird to feed several books into an AI and have it output a schedule, since the table of contents of each book is itself a schedule, and many such schedules already exist

it's fine ig. I don't think it makes a huge difference having a list like this, since most books and degree programs would already follow a cleaner version of this progression? I don't see the point but you do you ig

[latent thorn]

well i used 2 book and my country program

and to complete the list i combined them both

[gray gazelle]

I feel like you could just go through both books and talk to an advisor from that program or look at a sample course schedule from that program and it'd be more accurate

like most AI things, the list looks roughly fine as a general idea but if you tried to follow it completely strictly you'd probably be worse off (i.e., doing differentiation before trig)

[latent thorn]

mh I see, so from the outside it looks fine but when i start following the list i will be lost

[gray gazelle]

for example, if you have a book that goes over sets, it will probably mention functions as well as logic

[latent thorn]

oh i see

[gray gazelle]

not to say that it will go through functions on the same level as an analysis textbook

but you'd learn at least a little bit about them

[latent thorn]

thats a bit annoying.. Because i try to make some notes abt all of this and then do a lot of exercices, well u get what i mean anyway

[gray gazelle]

I think that's a good approach, I would just keep in mind that AI guidance < textbook/video guidance < advisor/professor guidance, if that makes sense

I don't think you can go wrong just picking a good book and following it tbh, especially if that book is in your program

like the idea that percentages requires its own special unit is weird. AI gives all sorts of weird perspectives like that. like yes percentages come up a lot, but if you know basic algebra they're really just a footnote

imo anyway

[latent thorn]

Okay okay

[hybrid sigil]

This one is fun :)

Maybe too practical

I think a more valuable thing to put in your CV is a link to your own compiler on GitHub

You need to write it first though

[latent thorn]

bahaha

[hybrid sigil]

But it’s easy to start with this book

[latent thorn]

put ur entire personal OS

they will be impressed

as they should

just fake ur resume tho thats what my president say

[hybrid sigil]

Well, fair enough, but this book has two parts

[latent thorn]

if u dont have knowledge, invent it

[hybrid sigil]

First one is interpreter, the second one is a byte code VM implementation

So you need to compile to your byte code

Also, the first part is in Java, the second — in C

You also do GC, OOP and stuff

It’s of course lighter on optimisation and theory

[latent thorn]

the best language is assembly anyway

always remember that guys

fell for that propaganda

[hybrid sigil]

I’ve also got this, but to be honest, didn’t read it much since I bought it :)

But I hope it’s good, otherwise why would I choose it?)

Yeah, the best way to demonstrate that I think they are decent :)

I also worked professionally in compilers/interpreters area for 5+ years (not anymore though), so let me know if you have questions

[pearl palm]

How many books do you have???

[hybrid sigil]

Not that many, maybe 3 shelves on math, computer science and programming

[hybrid sigil]

We had to implement type checkers, so technically yes :) one type system was based on Row polymorphism: https://en.wikipedia.org/wiki/Row_polymorphism?wprov=sfti1

Which, as Wikipedia says, can be informally described as “static duck typing" :)

We needed something that doesn’t require many explicit type annotations and is easy to use for the users of that language that we were developing, but still wanted static type checking guarantees

Plus, most people I worked with were quite enamoured with type theory, dependent types, and dived deep into languages like Idris, Agda, sometimes theorem provers too

Haven’t read that. Looks interesting, yes. Somewhat worrying are minor complaints about the language (like it feels that it was translated) in Amazon reviews

I hope it’s not like those automatically translated books that Springer produces sometimes…

I mean books that sound like German literally translated to English word by word, plus some weird punctuation. For example Marco Hien “Abstract Algebra”

I guess they are better than no translation at all, but I’m not a fan

[remote sparrow]

i think the authors are dutch

but not 100% sure, the book only says they worked in the netherlands

[hybrid sigil]

Sorry, I meant Springer books, not the one that Mr Chipper mentioned. Updated my message

An example of what I mean is Marco Hien “Abstract Algebra”

[remote sparrow]

gotcha

[hybrid sigil]

Interestingly enough Honest Torus shows this book in his video (saying that it’s one of the books that gives algebra some motivational path, in this case via Galois theory, I think), but he doesn’t mention any issues with translation

So it looks like he is either not bothered by that or just didn’t read the book :)

[hybrid sigil]

This one looks promising: an overview of foundations needed for theorem provers: https://arxiv.org/abs/2009.09541

This is from one of the professors from OpenLogic project

[plain barn]

any recs on diff geo from a sheaf perspective?

in general does anyone have any recs for diff geo that isn't Tu

[vital bane]

@daring wolf

[plain barn]

wonder if "manifold" knows something about this

[daring wolf]

https://link.springer.com/book/10.1007/978-3-658-10633-1

[plain barn]

thx

[past dust]

Good resources for conic sections specially ellipses ?

[plucky flint]

Could you please share the server rules? I've forgotten them.

[tender cobalt]

https://discord.com/channels/268882317391429632/486128019652476939

[plucky flint]

Thanks.

[tender cobalt]

Also could literally just check table of contents of the assigned book and syllabus?

[peak dawn]

Yeah absolutely

[thick gyro]

any books for Calculus II - III? Stewart's Calculus is nice and all, but it sometimes unnecessarily lengthens a topic

[molten gulch]

Thomas calc, larson calc

[thick gyro]

man i wish i bough thomas' calculus instead of Stewart's

that one indeed looks nice and small

[molten gulch]

It's just as long

[thick gyro]

overall it's the same but
limits

• stewart: 100p
• thomas: 60p
  derivatives
• stewart: 100p
• thomas: 80p

this could've saved me some time.

[vital chasm]

If you want conciseness go for lecture notes

[thick gyro]

you mean like paul's online math notes?

[vital chasm]

Nobody bothers to type 800 pages for a course

[vital chasm]

Thats the one I was thinking of but one cam probably find shorter

[molten gulch]

Vakil's AG notes when they started as 60 pages and are now 900 (600 in book typesetting)

[thick gyro]

also, will this hinder understanding?

[molten gulch]

No

But you might need to supplement examples

[barren carbon]

Hello, people. How are you? I'm from Brazil and I gonna join a Computational Mathematics

graduation at UFMG. I need your help to know about websites where I can buy virtual books about Math and related by a good price. If anyone can help, i gonna be glad (and correct me if my english is too bad, hehe).

[ancient creek]

How was it? haha

[tired glen]

Hey everyone. I am currently a beginner in linear algebra so I want to know how to learn it from basics. Yes I even don't know what is matrces and determinants too. Help me by suggesting some book. Thanks

[shut geode]

friedberg insel and spence is the standard rec, hoffman and kunze is also good

[inland pier]

Book recommendations to learn college mathematics from Scratch

[mortal iris]

Start with Johnston's Intro to Linear and Matrix Algebra.

[elder nymph]

Best Math book is Rs Agrwaal

[molten gulch]

Indian books are usually good for Indian maths curricula, not globally

[wet sentinel]

advanced linear algebra by roman is the way to go

[elder nymph]

Acha bate

[molten gulch]

speak english here only please

If you read the rules you'd know languages besides english are strictly prohibited in this server outside of the help channels and occasionally in the topic channels when someone asks a question in another language

[odd cargo]

yea bruh its game over

euler has got to be the greatest to ever do it

[molten gulch]

????

[broken cliff]

Hi guys.

I want to learn real math at a pre-university or high school level. I want to truly understand it and not just operate it like a machine. And I have significant difficulties in performing even basic mathematical operations. In other words, my level is basic or insufficient to get a good grade on a pre-university exam.

What resources do you recommend?

[unborn sinew]

I’ve never read a book because I don’t like reading, but I need something interesting that won’t bore me even once

[odd cargo]

what do you want from me

[chilly wolf]

Are there videos about the ket quantum, the properties and the <psi|psi> with guidance and explanation like beginners?

[glass tapir]

for an introduction into algebraic topology, which book would you guys recommend? I've started reading Rotman but I've been told Hatcher is the more popular book. Which books would you recommend (taking into account how they handle the prerequisites)?

for context, the only relevant courses I've taken are basic point set topology, as well as basic group and ring theory

[hybrid sigil]

You know that Hatcher is free, right? Why not to download it and compare with Rotman?

And here is what Hatcher himself recommends: https://pi.math.cornell.edu/~hatcher/Other/topologybooks.pdf

Unsurprisingly, his book 😅 but some others too

[molten gulch]

rotman is good, it's a bit slower than hatcher, but it introduces categories and such much earlier

[chrome mica]

What do you think of Discrete Mathematics: An Open Introduction 4th ed by Oscar Levin?
Here it is https://discrete.openmathbooks.org/dmoi4.html
I'm reading How to Prove It and I know there may be overlaps but I really like discrete math 🙂

[gray gazelle]

I would recommend arithmetic by paul lockhart, as well as his other books. I'm not sure others would (it's a bit closer to a pop math book; most people would recommend textbooks), but I feel his explanations are super simple, very inviting, and idk, I just feel he has a knack for presenting fundamental things in a very folksy way without losing much, if any, mathematical detail

that would be like, the most beginner entry possible. you could also look into basic mathematics by serge lang which is very rigorous, or even book of proof which is free and has a great intro to logic/sets, which I think really helps with understanding why things work

understanding is kind of elusive but I think if you read a variety of algebra or geometry resources, or history thereof, you'll start to see how certain basic axioms (think of these like fundamental rules) can create a ton of complexity and questions, which can lead to theorems (certain things that follow from axioms; nonobvious conclusions). concluding new things from basic rules is I think where you'd find what you're looking for, but ultimately just treat it as a marathon and not a sprint and you'll start to see connections and patterns, same as anything else in that regard (though maybe someone else has a different opinion?).
(and sorry for the big text wall lol)

[hybrid sigil]

Also there is this pinned recommendation: #book-recommendations message

[remote sparrow]

https://www.webtoons.com/en/drama/like-mother-like-daughter/list?title_no=5734

goated series

[gleaming viper]

any good books to practice 2d vector addition?

[hybrid sigil]

find the sum of two vectors: (6, 7) + (8, 9)

not entirely sure what is there to practice? It's just adding two pairs of numbers together?